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Conductance Distributions in Random Resistor Networks: Self Averaging and Disorder Lengths
- Publication Year :
- 1994
-
Abstract
- The self averaging properties of conductance $g$ are explored in random resistor networks with a broad distribution of bond strengths $P(g)\simg^{\mu-1}$. Distributions of equivalent conductances are estimated numerically on hierarchical lattices as a function of size $L$ and distribution tail parameter $\mu$. For networks above the percolation threshold, convergence to a Gaussian basin is always the case, except in the limit $\mu$ --> 0. A {\it disorder length} $\xi_D$ is identified beyond which the system is effectively homogeneous. This length diverges as $\xi_D \sim |\mu|^{-\nu}$ ($\nu$ is the regular percolation correlation length exponent) as $\mu$-->0. This suggest that exactly the same critical behavior can be induced by geometrical disorder and bu strong bond disorder with the bond occupation probability $p$$\mu$. Only lattices at the percolation threshold have renormalized probability distribution in a {\it Levy-like} basin. At the threshold the disorder length diverges at a vritical tail strength $\mu_c$ as $|\mu-\mu_c|^{-z}$, with $z=3.2\pm 0.1$, a new exponent. Critical path analysis is used in a generalized form to give form to give the macroscopic conductance for lattice above $p_c$.<br />Comment: 16 pages plain TeX file, 6 figures available upon request.IBC-1603-012
- Subjects :
- Physics
Self-averaging
Gaussian
Condensed Matter (cond-mat)
FOS: Physical sciences
Conductance
Statistical and Nonlinear Physics
Percolation threshold
Condensed Matter
law.invention
symbols.namesake
law
Lattice (order)
Exponent
symbols
Probability distribution
Resistor
Mathematical Physics
Mathematical physics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....9dad3c0abf44cf07daad191b669eabac